GCF of 9828/308, 9476/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9828/308, 9476/420 i.e 4/4620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9828/308, 9476/420.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 9828/308,9476/420?
Given fractions are 9828/308,9476/420
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 9828/308,9476/420, numerators are 9828,9476
Denominators are 308,420
The GCF of 9828,9476 is 4 .
LCM of 308,420 is 4620.
The greatest common factor of 9828/308,9476/420 = [GCF of 9828,9476]/[LCM of 308,420]= 4/4620
Therefore, the GCF of 9828/308,9476/420 is 4/4620.
To find the highest common factor of 9828,9476, we have to find the factors of both numbers and list the highest common factor.
The factors of 9828 are 1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 26, 27, 28, 36, 39, 42, 52, 54, 63, 78, 84, 91, 108, 117, 126, 156, 182, 189, 234, 252, 273, 351, 364, 378, 468, 546, 702, 756, 819, 1092, 1404, 1638, 2457, 3276, 4914, 9828
The factors of 9476 are 1, 2, 4, 23, 46, 92, 103, 206, 412, 2369, 4738, 9476
The HCF of 9828,9476 is 4.
Lets's calculate GCF of 9828,9476
| 2 | 9828, 9476 |
| 2 | 4914, 4738 |
| 2457, 2369 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 9828,9476 By Matching Biggest Common Factor Method
Now, list down the factors of 9828
:1,2,3,4,6,7,9,12,13,14,18,21,26,27,28,36,39,42,52,54,63,78,84,91,108,117,126,156,182,189,234,252,273,351,364,378,468,546,702,756,819,1092,1404,1638,2457,3276,4914,9828
Now, list down the factors of 9476
:1,2,4,23,46,92,103,206,412,2369,4738,9476
Greatest Common Factor
We found the factors 9828,9476 . The biggest common factor number is the GCF number.
So the greatest common factor 9828,9476 is 4.
Lets's calculate LCM of 308,420
| 2 | 308, 420 |
| 2 | 154, 210 |
| 7 | 77, 105 |
| 11, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 11 x 15 = 4620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/4620
Therefore, the GCF of Fractions 9828/308,9476/420 is 4/4620
Least Common Multiple of 308,420 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 308,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(308,420) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(308,420) x common factors =28 x 1 = 28
LCM(308,420) = ( 308 × 420 ) / 28
LCM(308,420) = 129360 / 28
LCM(308,420) = 4620
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 9828/308, 9476/420
1. What is the HCF of 9828,9476?
The HCF of 9828,9476 is 4
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 9828/308, 9476/420?
Answer: GCF of Numerators as per given numbers 9828/308, 9476/420 is
GCF of Numerators i.e. for 9828,9476 is 4
LCM of denominators i.e. for 308,420 is 4620.
Thus, GCF of Fractions is 4/4620.Finally, GCF of Fractions for 9828/308, 9476/420 is 4/4620.